Bell Labs

About: Bell Labs is a based out in . It is known for research contribution in the topics: Laser & Optical fiber. The organization has 36499 authors who have published 59862 publications receiving 3190823 citations. The organization is also known as: Bell Laboratories & AT&T Bell Laboratories.

Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models

Abstract: Best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known. If the true values are replaced by estimated values, the mean squared errors of the estimators of the fixed and random effects increase in size. The magnitude of this increase is investigated, and a general approximation is proposed. The performance of this approximation is investigated in the context of (a) the estimation of the effects of the balanced one-way random model and (b) the estimation of treatment contrasts for balanced incomplete block designs.

Spherical Model of Shallow Acceptor States in Semiconductors

Abstract: The effective-mass approximation for shallow acceptor states in cubic semiconductors with degenerate valence bands is reformulated. The Hamiltonian is written as the sum of a spherical term and a cubic corection, thus pointing out the relevance of the spherical symmetry in the acceptor problem and the strong similarity to the case of atoms with the spin-orbit interaction. Without the introduction of any explicit representation of the Hamiltonian, the present formulation yields a meaningful classification of the acceptor states and reduces the eigenvalue problem to simple radial Hamiltonians. These radial Hamiltonians are explicitly given for the most improtant acceptor states and are shown to apply also to the description of the exciton problem. The variational method is used in the numerical calculation. The resulting eigenvalues, eigenfunctions, and related quantities are given as functions of the relevant parameters. The theoretical ionization energies are compared with available experimental data.

On bandwidth

Abstract: It is easy to argue that real signals must be bandlimited. It is also easy to argue that they cannot be so. This paper presents one possible resolution of this seeming paradox. A philosophical discussion of the role of mathematical models in the exact sciences is given and a new formulation of the 2 WT theorem is presented. The paper is a written version of the second Shannon Lecture given at the 1974 International Symposium on Information Theory. An appendix giving proof of the 2 WT theorem has been added.

Double Hysteresis Loop of BaTi O 3 at the Curie Point

Abstract: It is known that the Curie point $\ensuremath{\theta}$ of the ferroelectric BaTi${\mathrm{O}}_{3}$ shifts to higher temperatures when a dc bias field is applied. If the crystal shows a sharp transition, we expect by applying an ac field at the Curie temperature that the crystal would become alternately ferroelectric and nonferroelectric in the cycle of the ac field. This can be seen in the shape of the hysteresis loop at temperatures slightly above $\ensuremath{\theta}$. In the center of the polarization $P$ versus field $E$ plot, we observe a linear behavior corresponding to the paraelectric state of BaTi${\mathrm{O}}_{3}$ above $\ensuremath{\theta}$. At both high voltage ends, however, we observe a hysteresis loop corresponding to the ferroelectric state. A change in temperature causes a change in size and shape of the double hysteresis loops, ranging from a line with curves at the ends (higher temperature) to two overlapping loops (lower temperature). The results obtained allow us to calculate the different constants in the free-energy expression of Devonshire and Slater. One of the results shows that the transition is of the first order since the ${P}^{4}$ term turns out to be negative. The properties of the hysteresis loops are discussed, especially the large spontaneous electrical polarization and the low coercive field strength.